Question

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Answer 1

Question:

A bus starting from rest moves with a uniform acceleration of 0.1 m/s² for 2 minutes. Find (a) the speed acquired, (b) the distance travelled.

Answer:

$\boxed{\mathfrak{(i) \ Speed \ acquired = 12 \ m/s}}$

$\boxed{\mathfrak{(ii) \ Distance \ travelled = 720 \ m}}$

Given:

Initial velocity (u) = 0 m/s

Time taken (t) = 2 minutes = 120 seconds

Acceleration (a) = 0.1 m/s²

To Find:

(i) Speed acquired i.e. Final velocity (v)

(ii) Distance travelled (s)

Explanation:

$\sf (i) \ From \ 1^{st} \ equation \ of \ motion: \\ \boxed{ \bold{v = u + at}}$

Substituting value of u, a & t in the equation:

$\sf \implies v = 0 + 0.1 \times 120 \\ \\ \sf \implies v = 0.1 \times 120 \\ \\ \sf \implies v = 12 \: m/s$

$\therefore$

Speed acquired i.e. Final velocity (v) = 12 m/s

$\sf (i) \ From \ 2^{nd} \ equation \ of \ motion: \\ \boxed{ \bold{s = ut + \frac{1}{2} a {t}^{2} }}$

Substituting value of u, a & t in the equation:

$\sf \implies s = 0 \times 120 + \frac{1}{2} \times 0.1 \times {(120)}^{2} \\ \\ \sf \implies s = 0 + \frac{1}{2} \times 0.1 \times 14400 \\ \\ \sf \implies s = \frac{1}{2} \times 0.1 \times 14400 \\ \\ \sf \implies s = \frac{1}{2} \times 1440 \\ \\ \sf \implies s = 720 \: m$

$\therefore$

Distance travelled (s) = 720 m

Question:

A racing car has a uniform acceleration of 4 m/s². What distance will it cover in 10 s after it start.

Answer:

$\boxed{\mathfrak{ Distance \ covered = 200 \ m}}$

Given:

Initial velocity (u) = 0 m/s

Acceleration (a) = 4 m/s²

Time taken (t) = 10 s

To Find:

Distance covered (s) by racing car

Explanation:

$\sf \ From \ 2^{nd} \ equation \ of \ motion: \\ \boxed{ \bold{s = ut + \frac{1}{2} a {t}^{2} }}$

Substituting value of u, a & t in the equation:

$\sf \implies s = 0 \times 10 + \frac{1}{2} \times 4 \times {(10)}^{2} \\ \\ \sf \implies s = 0 + \frac{1}{2} \times 4 \times 100 \\ \\ \sf \implies s = \frac{1}{2} \times 4 \times 100 \\ \\ \sf \implies s = \frac{1}{2} \times 400 \\ \\ \sf \implies s = 200 \: m$

$\therefore$

Distance covered (s) by racing car = 200 m

Answer 2

Answer:

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