Question

A bike moving along a straight road covers $35$ m in the $4$th second and $40$ m in the $5$th second. What is its initial velocity and acceleration (if the acceleration is assumed to be uniform )?

• A. ${17.5ms}^{-1}$
• B. ${8ms}^{-1}$
• C. ${7.8ms}^{-1}$
• D. ${38.5ms}^{-1}$

Answer 1

The correct option is A ${17.5ms}^{-1}$

Distance covered in $nth$ second is given by $S_n=u+\frac{1}{2}(2n-1)$

Case 1 : $n=4$ $S_n=35$

So, $35=u+\frac{a}{2}(2\times 4-1)$

Or $35=u+3.5n$ ......(1)

Case 2 : $n=5$ $S_n=40$

So, $40=u+\frac{a}{2}(2\times 5-1)$

Or $40=u+4.5n$ ......(2)

Equation (2) - (1), we get $40-35=4.5a-3.5a$

Or $a=5m/s^2$

Now, $35=u+3.5\times 5$

$⟹u=17.5m/s$