Question

The distance travelled in seconds by 'object' starting with a speed of $u$ metres/second and moving along a straight line with speed increasing at the rate of $a$ metres/second every second is given by $ut+\frac{1}{2}a{t}^2$. An object moving in this manner travels $10$ metres in $2$ seconds and $28$ metres in $4$ seconds. With what speed did it start? At what rate does its speed change?

Answer 1

Given $S=ut+\frac{1}{2}a{t}^2.....\left(1\right)$

Case:1 $S=10m$ and $t=2sec$

Putting value of S and t in equation 1

$\therefore 10=2u+2a\Rightarrow u+a=\mathrm{5....}\left(2\right)$

Case:2 $S=28m$ and $t=4sec$

Putting value of S and t in equation 1

$\therefore 28=4u+8a\Rightarrow 2u+4a=\mathrm{14....}\left(3\right)$

Multiplying equation (2) by a and subtracting from equation (3)

$2u+4a=14$

$\underset{–}{-2u-2a=-10}$

$2a=4\Rightarrow a=2$

Putting the value of a in equation (2)

$u+a=5\Rightarrow u=5-a=5-2=3$