A train accelerates uniformly along a straight track from an initial velocity of 10\text{ … — JAMB UTME

A train accelerates uniformly along a straight track from an initial velocity of $10\text{ m/s}$ to a final velocity of $30\text{ m/s}$ over a distance of $100\text{ m}$ . What is the magnitude of the acceleration of the train?

A
$0.2\text{ m/s}^2$
$4\text{ m/s}^2$ Answer
C
$5\text{ m/s}^2$
D
$8\text{ m/s}^2$

Answer

4\text{ m/s}^2

Using the equation of motion

v^2 = u^2 + 2as

, substitute

u = 10\text{ m/s}

v = 30\text{ m/s}

, and

s = 100\text{ m}

. This gives

30^2 = 10^2 + 2(a)(100)

, which simplifies to

900 - 100 = 200a

, or

800 = 200a

. Solving for acceleration yields

a = 4\text{ m/s}^2

Step-by-Step Solution

Identify the given kinematic values from the problem statement.

Initial velocity

u = 10\text{ m/s}

, final velocity

v = 30\text{ m/s}

, and displacement

s = 100\text{ m}

Listing known values helps in selecting the appropriate equation of motion.

Select the linear motion formula relating

u

v

s

, and acceleration

a

v^2 = u^2 + 2as

This formula connects initial velocity, final velocity, distance, and acceleration without requiring time

t

Substitute the values into the equation and solve for

a

30^2 = 10^2 + 2(a)(100) \implies 900 = 100 + 200a \implies 800 = 200a \implies a = 4\text{ m/s}^2

Algebraic rearrangement yields the magnitude of acceleration.

Key Concept

Equations of Uniformly Accelerated Motion

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic