Question

A car accelerates at 2.5 m/s2 to a velocity of 20 m/sec, then it travels at this constant velocity before decelerating at 4 m/s2. If the total distance covered was 500 m , how long will it take to cover the distance?

Answer 1

To find the time it takes for the car to cover a total distance of 500 meters, we can break down the motion into three phases: acceleration, constant velocity, and deceleration.

Phase 1: Acceleration The car accelerates at a rate of 2.5 m/s² until it reaches a velocity of 20 m/s. We can use the following kinematic equation to find the time taken during this phase:

$v=u+at$

Where:

• v is the final velocity (20 m/s)
• u is the initial velocity (0 m/s since it starts from rest)
• a is the acceleration (2.5 m/s²)
• t is the time

Plugging in the given values, we can solve for the time taken during the acceleration phase:

$20=0+2.5t$

$2.5t=20$

$t=\frac{20}{2.5}$

$t=8$

So, the time taken during the acceleration phase is 8 seconds.

Phase 2: Constant Velocity The car travels at a constant velocity of 20 m/s. To find the time taken during this phase, we can use the equation:

$t=\frac{d}{v}$

Where:

• d is the distance traveled during this phase (which is the total distance minus the distances covered during acceleration and deceleration)
• v is the constant velocity (20 m/s)

Plugging in the values, we get:

$t=\frac{500-0-0}{20}$

$t=\frac{500}{20}$

t=25<annotation encoding="a