Question

A cyclist is initially traveling at 12 m/s. He travels 32 m for the next 4 seconds. Determine (a) Its acceleration (b) its speed after 4 seconds

Answer 1

• a = -2m/s²

,

• v = 4m/s

Step-by-step explanation

Given:

• The initial speed of the cyclist, v₀ = 12 m/s

,

• The distance traveled, x = 32m

,

• The time interval, t = 4s,

Unknown

• The acceleration, a

,

• The speed after 4s, v

The distance the cyclist travels, assuming he is traveling with constant acceleration is,

`x=v_ot+(1)/(2)at^2`

We have to solve this equation for a. Subtract v₀t from both sides,

`x-v_ot=(1)/(2)at^2`

And divide both sides by 1/2t²,

`a=(2(x-v_ot))/(t^2)`

Replace with the given values,

`a=(2(32m-12m/s\cdot4s))/(4^2s^2)=(2(32m-48m))/(16s^2)=(2\cdot(-16)m)/(16s^2)=-2m/s^2`

Hence, the cyclist's acceleration is -2m/s².

The speed is,

`v=v_o+at=12m/s-2m/s^2\cdot4s=12m/s-8m/s=4m/s`

Hence, the final speed is 4m/s.