Question

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

• A. $112.5m$ and $22.5s$
• B. $337.5m$ and $25s$
• C. $112.5m$ and $15s$
• D. $225.5m$ and $10s$

Answer 1

Answer: (A)

$112.5m$ and $22.5s$

Distance covered by car in 15 sec=area under graph$=\frac{1}{2}\times 15\times 45=337.5m$

Distance covered by scooter$=15\times 30=450m$

Difference $=450-337.5=\underset{–}{112.5m}$

Distance covered by scooter in next 5 sec $=30\times 5=150m$

Distance covered by car in next 5 sec$=45\times 5=225m$

Total distance covered by car in 20 sec$=337.5+225=562.5m$

Total distance covered by scooter in 20 sec$=450+150=600m$

By hit and trial method it proves that after $\underset{–}{22.5s}$ they will meet each other.