Question

If your car accelerates from rest at a steady rate of, how soon will it reach \[90km/h\] \[(55.9mph\] or \[25m/s)?\]

Answer 1

Hint: To solve this question, we have to know about velocity, acceleration and the formula of velocity and acceleration properly. We know that acceleration is the rate of change of velocity. And we also know that the rate of change of speed is called the velocity. And also we have to calculate the whole thing in the same unit. Otherwise, the calculation will become incorrect, we have to keep that in our mind.

Complete step by step answer:
Let us consider the initial velocity u. which is zero, according to the question.Again, according to the question, acceleration is denote by a, which is equal to \[4m/{\sec ^2}\].And we can say, the final velocity is $v$ which is equal to \[25m{s^{ - 1}}\].Now we are going to apply the equation of motion which is given by, \[v = u + at\]. Now, from this equation we can say, time t is equal to, \[\dfrac{{v - u}}{a}\]. Now, putting the value of a, v and u we get,
\[\dfrac{{25 - 0}}{4} = 6.25s\]

So, the right answer is \[6.25s\].

Note: We can get confused between acceleration and acceleration due to gravity. We know that any acceleration which occurs due to gravitational force is called acceleration due to gravity. Acceleration equal to velocity by time. And we know that the velocity is equal to speed by time. so, we can say, the unit of acceleration is meters per second squared. And the unit of velocity is meter by second. These are the S.I units of acceleration and velocity.