Question

A car travelled a distance of 200 m with initial velocity of 216 km/hr. Calculate the acceleration

in meters per second of the car if it has a final velocity of 360 km/hr.

Answer 1

`a = 16\ m/s^2`

Step-by-step explanation:

When the velocity changes uniformly, the object has a constant acceleration. The acceleration, the velocities, and the distance are related by the equation:

`v_f^2=v_o^2+2ax`

Where:

vf = final velocity

vo = initial velocity

a = acceleration

x = distance

Solving for a:

`\displaystyle a=(v_f^2-v_o^2)/(2x)`

The car travels a distance of x=200 m and the velocities are:

vo = 216 Km/h

vf = 360 Km/h

Both velocities must be converted to meters by seconds.

vo = 216 Km/h *1000/3600 = 60 m/s

vf = 360 Km/h *1000/3600 = 100 m/s

The acceleration is:

`\displaystyle a=(100^2-60^2)/(2*200)`

`\displaystyle a=(10000-3600)/(400)`

`\displaystyle a=(6400)/(400)`

`\mathbf{a = 16\ m/s^2}`