Question:
A bus is moving with a speed of $ 10 \,ms^{-1} $ on a straight road. A scooterist wishes to overtake the bus in $ 100 \,s $ . If the bus is at a distance of $ 1 \,km $ from the scooterist with what speed should the scooterist chase the bus ?
A bus is moving with a speed of $ 10 \,ms^{-1} $ on a straight road. A scooterist wishes to overtake the bus in $ 100 \,s $ . If the bus is at a distance of $ 1 \,km $ from the scooterist with what speed should the scooterist chase the bus ?
Updated On: May 3, 2024
- $ 40 \,ms^{-1} $
- $ 25 \,ms^{-1} $
- $ 10 \,ms^{-1} $
- $ 20 \,ms^{-1} $
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The Correct Option is D
Solution and Explanation
Let $v$, be the velocity of the scooter, the distance between the scooter and the bus $=1000\, m$,
The velocity of the bus $=10\, ms ^{-1}$
Time taken to overtake $=100\, s$
Relative velocity of the scooter with respect to the bus $=\left( v _{ s }-10\right)$
$1000 /\left(v_{s}-10\right)=100\, s$
$=v_{s}=20\, ms ^{-1}$
The velocity of the bus $=10\, ms ^{-1}$
Time taken to overtake $=100\, s$
Relative velocity of the scooter with respect to the bus $=\left( v _{ s }-10\right)$
$1000 /\left(v_{s}-10\right)=100\, s$
$=v_{s}=20\, ms ^{-1}$
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.