Question

The minimum time taken by a car to come to rest in a distance of 1.2 km from standstill is 2 minutes. What is the maximum velocity of the car?

Answer 1

To find the maximum velocity of the car, we can use the equation of motion that relates distance, initial velocity, acceleration, and time. The equation is:

$d=ut+\frac{1}{2}a{t}^2$

Where:

• $d$ is the distance traveled (1.2 km, which is equivalent to 1200 meters),
• $u$ is the initial velocity (0 m/s since the car starts from standstill),
• $a$ is the acceleration (unknown in this case),
• $t$ is the time taken (2 minutes, which is equivalent to 120 seconds).

Rearranging the equation, we have:

$d=\frac{1}{2}a{t}^2$

Solving for acceleration $a$:

$a=\frac{2d}{t^2}$

Plugging in the values:

$a=\frac{2\times 1200}{120^2}$