Question

An object starting from rest travels 20 m in the first 2 s and 160 m in the next 4 s. What will be the velocity after 7 s from the start?

Answer 1

Step (1) Given:

The object starts from rest. Hence, its initial velocity, $u=0m/s$

time taken by the object, $t=2s$

Distance covered by the object, $s=20m$

Step (2) Finding the acceleration produced in the object:

According to the second equation of motion,

$$\begin{gathered} s=ut+\frac{1}{2}a{t}^2 \\ 20=0+\frac{1}{2}\times a\times 2^2 \\ 20=\frac{1}{2}\times a\times 2^2 \\ 20=\frac{1}{2}\times a\times 4 \\ 20=2a \\ a=10m/s^2 \end{gathered}$$

Step (3) Finding the velocity of the object after 7 seconds:

According to the first equation of motion velocity after 7 s from the start

$$\begin{gathered} v=u+at \\ v=0+10\times 7 \\ v=70m/s \end{gathered}$$