Question

the question I need help on is Your teacher's car can go from rest to 25 m/s (≈60mph) in 10 seconds. The car's velocity changes at a uniform rate. How fast is the car going 6 seconds after it starts?

Answer 1

Given,

The initial velocity of the car, u=0 m/s

The final velocity of the car after 10 seconds, v₁=25 m/s

The time periods, t₁=10 s

and t₂=6s

First, we need to find the acceleration of the car, in order to find the velocity of the car after 6 seconds.

From the equation of the motion,

$v_1=u+at_1$

Where a is the acceleration of the car.

On substituting the known values in the above equation,

$\begin{gathered} 25=0+a\times10 \\ \Rightarrow a=\frac{25}{10} \\ =2.5m/s^2 \end{gathered}$

To find the velocity of the car after 6 seconds, we use an equation of the motion,

$v_2=u+at_2$

On substituting the known values,

$\begin{gathered} v_2=0+2.5\times6_{} \\ =15\text{ m/s} \end{gathered}$

Therefore the acceleration of the car after 6 seconds is 15 m/s.