Question

What is the acceleration of a mountain bike if it slows down from 9.4 m/s to 3.0 m/s in a time of 3.75 s?

A bicycle slowing down from 20 m/s to 15 m/s in 6 seconds. Calculate the acceleration














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Answer 1

Solution :-

Required formula :

• $\bigstar{ \boxed{ \tt{\red{a = \dfrac{v-u}{t}}}}} \bigstar$

• $\bigstar{ \boxed{ \tt{\blue{v =u+at}}}} \bigstar$

We can use any of these formula for solving this question.

In First Question :

Given,

• Initial Velocity (u) = 9.4 m/s
• Final Velocity (v) = 3.0 m/s
• Time taken (t) = 3.75 s

To Find,

• Acceleration of the mountain bike (a).

Substituting the values :

$: \implies{ \sf{3.0 = 9.4+ a \times 3.75}}$

$: \implies{ \sf{3.0= 9.4+ 3.75a}}$

$: \implies{ \sf{3.0 - 9.4 = 3.75a}}$

$:\implies{ \sf{ - 6.4 = 3.75a}}$

$:\implies{ \sf{ \dfrac{ - 6.4}{3.75} = a}}$

$: \implies{ \sf{ -1.70..... = a}}$

$:\implies{ \boxed{ \tt{\pink{ a = -1.7 \: m/s^2 \: (approx)}}}}$

∴ Acceleration of the mountain bike = -1.7 m/s^2.

In Second Question :

Given,

• Initial Velocity (u) = 20 m/s
• Final Velocity (v) = 15 m/s
• Time taken (t) = 6 s

To Find,

• Acceleration of the bicycle (a).

Substituting the values :

$: \implies{ \sf{15= 20+ a \times 6}}$

$: \implies{ \sf{15= 20+ 6a}}$

$: \implies{ \sf{15 - 20 = 6a}}$

$: \implies{ \sf{ - 5 = 6a}}$

$: \implies{ \sf{ \dfrac{ -5}{6} = a}}$

$: \implies{ \sf{ -0.83...... = a}}$

$:\implies{ \boxed{ \tt{\pink{ a = -0.83 \: m/s^2 \:(approx)}}}}$

∴ Acceleration of the bicycle = -0.83 m/s^2 .