A particle traveling along a straight line accelerates uniformly from an initial speed u t… — JAMB UTME

A particle traveling along a straight line accelerates uniformly from an initial speed $u$ to a final speed of $25\text{ m/s}$ over a distance of $150\text{ m}$ in a time duration of $8\text{ s}$ . What is the initial speed $u$ in $\text{m/s}$ ?

Answer: 12.5 m/s

Answer

The initial speed of the particle is

12.5\text{ m/s}

Under uniform acceleration, displacement is given by the product of average velocity and time:

s = \frac{u + v}{2}t

. Substituting

s = 150\text{ m}

v = 25\text{ m/s}

, and

t = 8\text{ s}

gives

150 = 4(u + 25)

, which yields

u = 12.5\text{ m/s}

Step-by-Step Solution

Identify the given parameters and select the appropriate kinematic equation.

Givens:

s = 150\text{ m}

v = 25\text{ m/s}

t = 8\text{ s}

. Formula:

s = \frac{u + v}{2}t

This formula relates displacement directly to average velocity and time under uniform acceleration without needing the acceleration variable.

Substitute the given values into the formula.

150 = \left(\frac{u + 25}{2}\right) \times 8 = 4(u + 25)

Simplifying

\frac{8}{2}

gives a factor of

4

multiplying

(u + 25)

Isolate and solve for the unknown initial speed

u

u + 25 = \frac{150}{4} = 37.5 \implies u = 12.5\text{ m/s}

Subtracting

25

from

37.5

yields the value of

u

Key Concept

Kinematics with uniform linear acceleration

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