A car traveling along a straight road at an initial speed of 20\text{ m/s} applies its bra… — JAMB UTME

A car traveling along a straight road at an initial speed of $20\text{ m/s}$ applies its brakes, causing a uniform deceleration of $5\text{ m/s}^2$ until it comes to a complete stop. What is the total distance traveled by the car during this braking period?

Answer: 40 m

Answer

The total distance traveled by the car while coming to a stop is

40\text{ m}

Using the third equation of linear motion

v^2 = u^2 + 2as

with

u = 20\text{ m/s}

v = 0\text{ m/s}

, and acceleration

a = -5\text{ m/s}^2

, we obtain

0 = 400 - 10s

, which simplifies directly to

s = 40\text{ m}

Step-by-Step Solution

Identify the given kinematic parameters from the problem statement.

u = 20\text{ m/s}

v = 0\text{ m/s}

a = -5\text{ m/s}^2

The car decelerates to a stop, so final velocity is zero and acceleration is negative relative to initial direction of motion.

Select the appropriate equation of motion linking

u

v

a

, and displacement

s

v^2 = u^2 + 2as

This equation directly relates initial velocity, final velocity, acceleration, and distance without requiring time.

Substitute the known values into the equation and solve for distance

s

0^2 = 20^2 + 2(-5)s \implies 10s = 400 \implies s = 40\text{ m}

Algebraic simplification yields the stopping distance.

Key Concept

Uniformly Accelerated Motion and Stopping Distance

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