Question

A car that stands at a traffic signal starts its motion with acceleration\[5m{s^{ - 2}}\]. Then the velocity of the car after \[4s\] and distance traveled by car during this \[4s\]will be _____and_____ respectively.
\[(A)40m{s^{ - 1}},20m\]
\[(B)20m{s^{ - 1}},20m\]
\[(C)40m{s^{ - 1}},40m\]
\[(D)20m{s^{ - 1}},40m\]

Answer 1

Hint : The initial velocity of the car is zero since it starts from rest. Using the second equation of motion we can find the distance traveled by the car and therefore the velocity of the car can be found using the first equation of motion.

Formula used:
The first equation of motion\[v = u + at\]
The second equation of motion\[s = ut + \dfrac{1}{2}a{t^2}\]
Where,\[u\]is the initial velocity and \[v\]is the final velocity, \[a\]is the acceleration of car and \[t\]- time,
\[s\]- The distance traveled by car.

Complete step-by-step solution:
It is provided that the acceleration of a car is \[a = 5m{s^{ - 2}}\]
The car starts from rest so that the initial velocity of the car is zero. \[u = 0\]
Time \[t = 4s\]
Now allow us to find the velocity of the car after\[4s\] .
For this let us use the first equation of motion within the case of the car.
\[v = u + at\]
\[v = 0 + \left( {5 \times 4} \right) = 20m{s^{ - 1}}\]
We need to seek out the distance traveled by car during\[4s\] .
We all know that from the second equation of motion.
\[s = ut + \dfrac{1}{2}a{t^2}\]
\[s = 0 + \dfrac{1}{2}\left( {5 \times {4^2}} \right) = 40m\]
The velocity of the car after \[4s\]and distance traveled by car during this \[4s\]will be \[20m{s^{ - 1}}\]and \[40m\]respectively.
Hence, option D is correct.

Additional information: The three equations of motion form the basics of classical mechanics. The equations establish relations between the physical quantities that define the characteristics of motion of a body like the acceleration of the body, the displacement, and also the velocity of the body. \[a = \dfrac{{dv}}{{dt}},v = \dfrac{{ds}}{{dt}}\].

Note: Acceleration is termed as a vector quantity that defines the rate at which an object changes its velocity. An object continues to be accelerating if it is changing its velocity-time and again. Anytime an object's velocity is changing the object is said to be in an accelerating motion or it has acceleration.