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Question: An object at rest gains an average velocity of \[40\,{\text{m}} \cdot {{\text{s}}^{ - 1}}\] in 5 sec...

An object at rest gains an average velocity of 40 m⋅s−140\,{\text{m}} \cdot {{\text{s}}^{ - 1}} in 5 seconds. What will be its acceleration?

Explanation

Solution

Use the first kinematic equation for the final velocity of the object. This equation gives the relation between the final velocity of the object, initial velocity of object, acceleration of the object and time. The initial velocity of the object is zero. Rearrange this equation for acceleration of the object and substitute all the values in the formula to calculate acceleration of the object.

Formula used:
The kinematic equation for the final velocity vv of an object is given by
v=u+atv = u + at …… (1)
Here, uu is the initial velocity of the object, aa is acceleration of the object and tt is time.

Complete step by step answer:
We have given that the object gains an average velocity of 40 m⋅s−140\,{\text{m}} \cdot {{\text{s}}^{ - 1}} in the time duration of 5 seconds.
v=40 m⋅s−1v = 40\,{\text{m}} \cdot {{\text{s}}^{ - 1}}
⇒t=5 s\Rightarrow t = 5\,{\text{s}}
The object starts from rest. Hence, the initial velocity of the object is zero.
u=0 m⋅s−1u = 0\,{\text{m}} \cdot {{\text{s}}^{ - 1}}
We have asked to calculate the acceleration of the object.We can calculate the acceleration of the object using equation (1).Rearrange equation (1) for acceleration of the object.
a=v−uta = \dfrac{{v - u}}{t}
Substitute 40 m⋅s−140\,{\text{m}} \cdot {{\text{s}}^{ - 1}} for vv, 0 m⋅s−10\,{\text{m}} \cdot {{\text{s}}^{ - 1}} for uu and 5 s5\,{\text{s}} for tt in the above equation.
a=(40 m⋅s−1)−(0 m⋅s−1)5 sa = \dfrac{{\left( {40\,{\text{m}} \cdot {{\text{s}}^{ - 1}}} \right) - \left( {0\,{\text{m}} \cdot {{\text{s}}^{ - 1}}} \right)}}{{5\,{\text{s}}}}
⇒a=(40 m⋅s−1)5 s\Rightarrow a = \dfrac{{\left( {40\,{\text{m}} \cdot {{\text{s}}^{ - 1}}} \right)}}{{5\,{\text{s}}}}
∴a=8 m⋅s−2\therefore a = 8\,{\text{m}} \cdot {{\text{s}}^{ - 2}}

Hence, the acceleration of the object is 8 m⋅s−28\,{\text{m}} \cdot {{\text{s}}^{ - 2}}.

Note: One can also solve the same question by another method. One can directly take the ratio of the average velocity gained by the object and time required to gain this average velocity. But the students should keep in mind that this formula can be directly used only when the object starts from rest i.e. the initial velocity of the object is zero.