Question

The velocity-time graphs of a car and a scooter are shown in the figure. (i) the difference between the distance travelled by the car and the scooter in $15s$ and (ii) the time at which the car will catch up with the scooter are, respectively

• A. $337.5m$ and $25s$
• B. $225.5m$ and $10s$
• C. $112.5m$ and $22.5s$
• D. $\mathrm{11.2.5}m$ and $15s$

Answer 1

The correct option is C $112.5m$ and $22.5s$

The distance traveled in 15 seconds by both will be given by area under curve.

For car, $s_1=\frac{1}{2}\times 15\times 45$

$s_1=337.5m$

For scooter, $s_2=15\times 30$

$s_2=450$

$s_1-s_2=112.5m$

Suppose after time t, they will meet, then distance traveled by both of them will be equal.

$30t=\frac{1}{2}\times 15\times 45+45\times (t-15)$

$30t=337.5+45t-675$

$15t=337.5$

$t=22.5s$