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Motion in a Straight Line — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Straight Line3 Marks
Question
A bus starts with a constant acceleration 1ms-2. At the same time a car moving with a constant velocity of 5ms-1 overtakes the bus.
  1. How far from the starting point, the bus overtakes the car.
  2. How fast the bus was moving at the time of overtake?
✓

Answer

Initial velocity of bus, u = 0. Let the bus overtakes the car after time t.
$\therefore$ Distance travelled by bus in time t,
$\text{S}_\text{b}=\text{ut}+\frac{1}{2}\text{at}^2$
$=0+\frac{1}{1}\text{t}^2=\frac{\text{t}^2}{2}$ ($\because$ a = 1ms-2)
Distance travelled by car moving with constant velocity (a = 0),
$\text{S}_\text{c}=\text{ut}+\frac{1}{2}\text{at}^2=5\text{t}$ ($\because$ u = 5ms-1 and a = 0)
Since $\text{S}_\text{b}=\text{S}_c$
$\therefore \frac{\text{t}^2}{2}=5\text{t}$
$\text{t}=10\text{s}$
$\therefore$ Distance travelled by bus when it overtakes car,
$\text{S}_\text{b}=\text{ut}+\frac{1}{2}\text{at}^2$
$=0\times10+\frac{1}{2}\times(10)^2\text{s}=50\text{m}.$
Speed of bus, v = u + at
= 0 + 1 × 10
= 10ms-1.

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