Question 79: Motion in 1D

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 $$15$$ $$s$$ and (ii) the time at which the car will catch up with the scooter are, respectively.

Accepted Answer

Till 15 sec car has accelerative motion and scooter has constant velocity in entire motion.
Total Distance travelled by the car in 15 sec, = $${1 \over 2}$$ $$ 	imes $$ $${{45} \over {15}}$$ $$ 	imes $$ (15)
2
= $${{675} \over 2}$$ m
Distance travelled by scooter in 15 sec.
= V $$ 	imes $$ t = 30 $$ 	imes $$ 15 = 450 m
$$	herefore\,\,\,\,$$ Difference between distance travelled by the car and scooter in 15 sec,
= 450 $$-$$ $${{675} \over 2}$$ = 112.5 m
Now, assume car catches the scooter in time t,
$$	herefore\,\,\,\,$$ Car travelled in t sec = scooter travelled in t sec.
$$ \Rightarrow $$ $$\,\,\,\,$$ $${{675} \over 2}$$ + 45(t$$-$$ 15) = 30 $$ 	imes $$ t
$$ \Rightarrow $$ $$\,\,\,\,$$ 337.5 + 45t $$-$$ 675  = 30t
$$ \Rightarrow $$ $$\,\,\,\,$$ 15 t = 337.5
$$ \Rightarrow $$ $$\,\,\,\,$$ t = 22.5 sec.

Answer

$$112.5$$ $$m$$ and $$22.5$$ $$s$$

Answer

$$337.5$$ $$m$$ and $$25$$ $$s$$

Answer

$$112.5$$ $$m$$ and $$15$$ $$s$$

Answer

$$225.5$$ $$m$$ and $$10$$ $$s$$

Motion in 1D

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 $15 s$ and (ii) the time at which the car will catch up with the scooter are, respectively.

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