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

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Straight Line3 Marks
Question
A bus starts with a constant acceleration $1\ ms^{-2}$. At the same time a car moving with a constant velocity of $5\ ms^{-1}$ 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 $t, \text{S}_\text{b}=\text{ut}+\frac{1}{2}\text{at}^2$
$=0+\frac{1}{1}\text{t}^2=\frac{\text{t}^2}{2}$ ($\because a = 1\ ms^{-2}$)
Distance travelled by car moving with constant velocity $(a = 0)$, $\text{S}_\text{c}=\text{ut}+\frac{1}{2}\text{at}^2=5\text{t}$ $(\because u = 5\ ms^{-1}$ 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, $v = u + at = 0 + 1 \times 10 = 10\ ms^{-1}$.

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