Acceleration Worksheet - Weebly



Ch. 1.3 Acceleration Problems KEY

Name: Class: Date:

Acceleration is the rate of change in the speed of an object. To determine the rate of acceleration, you use the formula below. The units for acceleration are meters per second per second or m/s2.

[pic]

A positive value for acceleration shows speeding up, and negative value for acceleration shows slowing down. Slowing down is also called deceleration.

INSTRUCTIONS: Solve the below acceleration problems. Show all work by complete the boxes for each problem.

EXAMPLE

A skater skates in a straight line and increases her velocity from 2.0 m/s to 10.0 m/s in 3.0 seconds. What is the skater’s acceleration?

|1: Looking for: |4: Plug & Chug |

| |[pic] |

|the skater’s rate of acceleration |The acceleration of the skater is 2.7 meters per second every second. |

|2: Formula: | |

|[pic] | |

|3: State Givens & Assign Variables | |

| | |

|ν 1 = Initial speed = 2.0 m/s | |

| | |

|ν 2 = Final speed = 10.0 m/s | |

| | |

|Δt = Change in time = 3 seconds | |

1. While traveling along a highway a driver slows from 24 m/s to 15 m/s in 6 seconds. What is the automobile’s acceleration? (Remember that a negative value indicates a slowing down or deceleration.)

|1: Looking for: |4: Plug & Chug |

| | |

|the rate at which the driver decelerates |15 m/s - 24 m/s |

| |6 s |

| | |

| |= -9 m/s |

| |6 s |

| | |

| |= -1.5 m/s every s |

| | |

| |The driver slows down at a rate of 1.5 m/s every second. |

|2: Formula: | |

|[pic] | |

|3: State Givens & Assign Variables | |

| | |

|ν 1 = Initial speed = 24 m/s | |

| | |

|ν 2 = Final speed = 15 m/s | |

| | |

|Δt = Change in time = 6s | |

2. A parachute on a racing dragster opens and changes the speed of the car from 85 m/s to 45 m/s in a period of 4 seconds. What is the acceleration of the dragster?

|1: Looking for: |4: Plug & Chug |

| | |

|the rate at which the dragster decelerates |45 m/s - 85 m/s |

| |4 s |

| | |

| |= -40 m/s |

| |4 s |

| | |

| |= -10 m/s every s |

| | |

| |The dragster slows down at a rate of 10 m/s every second. |

|2: Formula: | |

|[pic] | |

|3: State Givens & Assign Variables | |

| | |

|ν 1 = Initial speed = 85 m/s | |

| | |

|ν 2 = Final speed = 45 m/s | |

| | |

|Δt = Change in time = 4 s | |

3. The table below includes data for a ball rolling down a hill at constant acceleration. Find the missing data values in the table and determine the acceleration of the rolling ball.

|Time (seconds) |Speed (km/h) |

|0 (start) |0 (start) |

|2 |3 |

|4 |6 |

|6 |9 |

|8 |12 |

|10 |15 |

|1: Looking for: |4: Plug & Chug |

| | |

|the rate of acceleration for rolling ball |15 km/hr - 3 km/hr |

| |8 s |

| | |

| |= 12 km/hr |

| |8 s |

| | |

| |= 1-1/2 m/s every s |

| | |

| |The rolling ball accelerates at a rate of 1-1/2 km/hr every second. |

|2: Formula: | |

|[pic] | |

|3: State Givens & Assign Variables | |

| | |

|ν 1 = Initial speed = 3 km/h | |

| | |

|ν 2 = Final speed = 15 km/hr | |

| | |

|Δt = Change in time = 10 s – 2 s = 8 s | |

4. A helicopter’s speed increases from 25 m/s to 60 m/s in 5 seconds. What is the acceleration of this helicopter?

|1: Looking for: |4: Plug & Chug |

| | |

|the helicopter’s rate of acceleration |60 m/s - 25 m/s |

| |5 s |

| | |

| |= 35 m/s |

| |5 s |

| | |

| |= 7 m/s every s |

| | |

| |The helicopter accelerates at a rate of 7 m/s every second. |

|2: Formula: | |

|[pic] | |

|3: State Givens & Assign Variables | |

| | |

|ν 1 = Initial speed = 25 m/s | |

| | |

|ν 2 = Final speed = 60 m/s | |

| | |

|Δt = Change in time = 5 s | |

5. As she climbs a hill, a cyclist slows down from 25 mi/hr to 7 mi/hr in 9 seconds. What is her deceleration? (finding acceleration; answer will be a negative)

|1: Looking for: |4: Plug & Chug |

| | |

|the rate at which the cyclist slows |7 mi/hr - 25 mi/hr |

| |9 s |

| | |

| |= 18 mi/hr |

| |9 s |

| | |

| |= -2 mi/hr every s |

| | |

| |The cyclist slows at a rate of 2 mi/hr every second. |

|2: Formula: | |

|[pic] | |

|3: State Givens & Assign Variables | |

| | |

|ν 1 = Initial speed = 25 mi/hr | |

| | |

|ν 2 = Final speed = 7 mi/hr | |

| | |

|Δt = Change in time = 9 s | |

6. After traveling for 5 seconds, a runner reaches a speed of 10 m/s. What is the runner’s acceleration?

|1: Looking for: |4: Plug & Chug |

| | |

|the runner’s rate of acceleration |10 m/s - 0 m/s |

| |5 s |

| | |

| |= 10 m/s |

| |5 s |

| | |

| |= 2 m/s every s |

| | |

| |The runner accelerates at a rate of 2 m/s every s. |

|2: Formula: | |

|[pic] | |

|3: State Givens & Assign Variables | |

| | |

|ν 1 = Initial speed = 0 m/s | |

| | |

|ν 2 = Final speed = 10 m/s | |

| | |

|Δt = Change in time = 5 s | |

7. A skateboarder traveling at 9 meters per second rolls to a stop at the top of a ramp in 3 seconds. What is the skateboarder’s acceleration?

|1: Looking for: |4: Plug & Chug |

| | |

|the skateboarder’s rate of acceleration |0 m/s - 9 m/s |

| |3 s |

| | |

| |= -9 m/s |

| |3 s |

| | |

| |= -3 m/s every s |

| | |

| |The skateboarder slows at a rate of 3 m/s every s. |

|2: Formula: | |

|[pic] | |

|3: State Givens & Assign Variables | |

| | |

|ν 1 = Initial speed = 9 m/s | |

| | |

|ν 2 = Final speed = 0 m/s | |

| | |

|Δt = Change in time = 3 s | |

8. A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts down the slope, its speed is 4 m/s. But 3 seconds later, at the bottom of the slope, its speed is 22 m/s. What is its average acceleration?

|1: Looking for: |4: Plug & Chug |

| | |

|the roller coaster’s rate of acceleration |22 m/s - 4 m/s |

| |3 s |

| | |

| |= 18 m/s |

| |3 s |

| | |

| |= 6 m/s every s |

| | |

| |The roller coaster picks up speed at a rate of 6 m/s every s. |

|2: Formula: | |

|[pic] | |

|3: State Givens & Assign Variables | |

| | |

|ν 1 = Initial speed = 4 m/s | |

| | |

|ν 2 = Final speed = 22 m/s | |

| | |

|Δt = Change in time = 3 s | |

9. A car advertisement states that a certain car can accelerate from rest to 70 km/hr in 7 seconds. Find the car’s average acceleration.

|1: Looking for: |4: Plug & Chug |

| | |

|the car’s rate of acceleration |70 km/hr - 0 km/hr |

| |7 s |

| | |

| |= 70 km/hr |

| |7 s |

| | |

| |= 10 m/s every s |

| | |

| |The car accelerates at a rate of 10 m/s every s. |

|2: Formula: | |

|[pic] | |

|3: State Givens & Assign Variables | |

| | |

|ν 1 = Initial speed = 0 km/hr | |

| | |

|ν 2 = Final speed = 70 km/hr | |

| | |

|Δt = Change in time = 7 s | |

10. A cyclist accelerates from 0 m/s to 9 m/s in 3 seconds. What is his acceleration ? Is this acceleration higher than that of a car which accelerates from 0 to 30 m/s in 6 seconds?

|1: Looking for: |4: Plug & Chug |

| | |

|the cyclist’s rate of acceleration |9 m/s - 0 m/s |

| |3 s |

| | |

| |= 9 m/s |

| |3 s |

| | |

| |= 3 m/s every s |

| | |

| |The cyclist’s rate of acceleration is 3 m/s every s. |

|2: Formula: | |

|[pic] | |

|3: State Givens & Assign Variables | |

| | |

|ν 1 = Initial speed = 0 m/s | |

| | |

|ν 2 = Final speed = 9 m/s | |

| | |

|Δt = Change in time = 3 s | |

|1: Looking for: |4: Plug & Chug |

| | |

|the car’s rate of acceleration |30 m/s - 0 m/s |

| |6 s |

| | |

| |= 30 m/s |

| |6s |

| | |

| |= g m/s every s |

| | |

| |The car’s rate of acceleration is 5 m/s every s. |

|2: Formula: | |

|[pic] | |

|3: State Givens & Assign Variables | |

| | |

|ν 1 = Initial speed = 0 m/s | |

| | |

|ν 2 = Final speed = 30 m/s | |

| | |

|Δt = Change in time = 6 s | |

Answer: The car’s rate of acceleration is greater than the cyclist.

11. You are traveling in a car that is moving at a velocity of 20 m/s. Suddenly, a car 10 meters in front of you slams on its brakes. At that moment, you also slam on your brakes and slow to 5 m/s. Calculate the acceleration if it took 3 seconds to slow your car down.

|1: Looking for: |4: Plug & Chug |

| | |

|the car’s rate of acceleration |5 m/s - 20 m/s |

| |3 s |

| | |

| |= -15 m/s |

| |3 s |

| | |

| |= -5 m/s every s |

| | |

| |The car slows its speed at a rate of 5 m/s every second. |

|2: Formula: | |

|[pic] | |

|3: State Givens & Assign Variables | |

| | |

|ν 1 = Initial speed = 20 m/s | |

| | |

|ν 2 = Final speed = 5 m/s | |

| | |

|Δt = Change in time = 2 s | |

12. A runner covers the last straight stretch of a race in 4 s. During that time, he speeds up from 5 m/s to 9 m/s. What is the runner’s acceleration in this part of the race?

|1: Looking for: |4: Plug & Chug |

| | |

|the runner’s rate of acceleration during this race section |9 m/s - 5 m/s |

| |4 s |

| | |

| |= 4 m/s |

| |4 s |

| | |

| |= 1 m/s every s |

| | |

| |The runner’s rate of acceleration during this part of the race is 1 m/s every s. |

|2: Formula: | |

|[pic] | |

|3: State Givens & Assign Variables | |

| | |

|ν 1 = Initial speed = 5 m/s | |

| | |

|ν 2 = Final speed = 9 m/s | |

| | |

|Δt = Change in time = 4 s | |

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