Question.
A bus starting from rest moves with a uniform acceleration of $0.1 \mathrm{~ms}^{-2}$ for 2 minutes. Find (a) the speed acquired. (b) the distance travelled.
A bus starting from rest moves with a uniform acceleration of $0.1 \mathrm{~ms}^{-2}$ for 2 minutes. Find (a) the speed acquired. (b) the distance travelled.
Solution:
Given
Initial speed of bus, $\mathrm{u}=0 \mathrm{~ms}^{-1}$
Final speed of bus, $v=$ ?
$\mathrm{a}=0.1 \mathrm{~ms}^{-2}, \mathrm{t}=2 \mathrm{~min}=120 \mathrm{~s}$
$\mathrm{s}=$ ?
(i) We know, $\mathrm{v}=\mathrm{u}+\mathrm{at}$
or $\mathrm{v}=0+0.1 \times 120=12 \mathrm{~ms}^{-1}$
(ii) $\mathrm{s}=\mathrm{ut}+\frac{1}{2} \mathrm{at}^{2}$
$\mathrm{s}=0 \times 120+\frac{1}{2} \times 0.1 \times(120)^{2}=720 \mathrm{~m}$
Therefore, final speed acquired $=12 \mathrm{~ms}^{-1}$
Distance travelled $=720 \mathrm{~m}$
Given
Initial speed of bus, $\mathrm{u}=0 \mathrm{~ms}^{-1}$
Final speed of bus, $v=$ ?
$\mathrm{a}=0.1 \mathrm{~ms}^{-2}, \mathrm{t}=2 \mathrm{~min}=120 \mathrm{~s}$
$\mathrm{s}=$ ?
(i) We know, $\mathrm{v}=\mathrm{u}+\mathrm{at}$
or $\mathrm{v}=0+0.1 \times 120=12 \mathrm{~ms}^{-1}$
(ii) $\mathrm{s}=\mathrm{ut}+\frac{1}{2} \mathrm{at}^{2}$
$\mathrm{s}=0 \times 120+\frac{1}{2} \times 0.1 \times(120)^{2}=720 \mathrm{~m}$
Therefore, final speed acquired $=12 \mathrm{~ms}^{-1}$
Distance travelled $=720 \mathrm{~m}$