acceleration kinematics

Question

1. A racecar accelerates at 5.0 m/s². If its initial velocity is 200 km/h, how far has it travelled after 8.0 s?
2. A car that starts from rest can travel a distance of 50 m in a time of 6.0 s.
3. What is the final velocity of the car?
4. What is the acceleration of the car?
5. A cyclist is travelling at 5.6 m/s when she starts to accelerate at 0.60 m/s² for a time interval of 4.0 s.
6. How far did she travel during this time interval?
7. What velocity did she attain?

Thank you:)

Answer 1

For problem 1:

a = 5.0 m/s²

Initial velocity is 200 km/hr but we need to convert to m/s (SI units)

200 km/hr x 1000 m/km x (1 hr)/(3600 sec) = 500/9 m/s (approx 55.56 m/s)

So v_i = 500/9 m/s

t = 8.0 s

Equation: x = v_it + (1/2)at²

x = (500/9)(8) + (1/2)(5)(8²) = 604 meters

For problem 2:

x = 50 m

t = 6 sec

v_i = 0 m/s (initially the car is "at rest")

Equation: x = v_it + (1/2)at²

50 = (0)(6) + (1/2)a(6²)

50 = 18a

a = 2.78 m/s²

To find the final velocity, use the equation: v_f = v_i + at

v_f = 0 + (2.78)(6) = 16.7 m/s

For problem 3:

v_i = 5.6 m/s

a = 0.60 m/s²

t = 4.0 sec

Use equation: x = v_it + (1/2)at²

x = (5.6)(4) + (1/2)(0.60)(4.0)²

x = 27.2 meters

To determine her final velocity, use equation v_f = v_i + at

v_f = 5.6 + (0.6)(4) = 8.0 m/s