# Kinematic equations in one dimension

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###### Lessons

**Applying kinematics equations to horizontal motion**- A sprinter accelerates from rest to 12.4 m/s in 9.58 s. What is the average acceleration of this sprinter?
- A commercial airplane must reach a speed of 75.0 m/s for takeoff. How long of a runway is needed if the acceleration is 3.20 m/s$^{2}$?
- A car traveling 15.0 m/s goes uphill with a uniform acceleration of -1.80 m/s$^{2}$. How far has it traveled after 5.00 s?
- How long does it take a car to decelerate from 85.0 km/h to 50.0 km/h in 100 m?

**Applying kinematics equations to vertical motion**- How long does it take a ball to hit the ground if it is dropped from a height of 1.50 m:
- on Earth, where acceleration due to gravity is 9.80 m/s$^{2}$?
- on the moon, where acceleration due to gravity is 1.62 m/s$^{2}$?

- A rock is thrown straight up with a speed of 20.0 m/s. How high does it go?
- A rock is thrown straight up with a speed of 20.0 m/s. How long is it in the air?
- A rock is thrown straight up with a speed of 20.0 m/s. When does the rock have a height of 15.0 m?
- A rock is thrown straight up with a speed of 20.0 m/s, and is caught when it comes back down.
- What is the velocity of the rock when it is caught?
- What is the velocity of the rock when it is at a height of 15.0 m? Include both $v$ as it goes up and $v$ as it comes back down.

- A ball is tossed straight up into the air with a speed of 12.0 m/s from the edge of a 324 m tall building.
- What is the impact speed of the ball as it hits the ground?
- What total distance did the ball travel?

- How long does it take a ball to hit the ground if it is dropped from a height of 1.50 m:
**Solving "two part" motion in one dimension**- A car travels at 23.5 m/s when the driver sees a deer on the road 55.0 m ahead of his car. It takes the driver 0.300 s of reaction time to hit the brakes, and the car starts decelerating at 6.40 m/s$^{2}$. Will the car stop in time to avoid hitting the deer?
- A falling stone takes 0.330 s to travel past a window 2.20 m tall. From what height above the top of the window did the stone fall?