A constant force of 12\text{ N} acts for 4.0\text{ s} on a body of mass 3.0\text{ kg} that… — JAMB UTME

A constant force of $12\text{ N}$ acts for $4.0\text{ s}$ on a body of mass $3.0\text{ kg}$ that is initially moving at $5.0\text{ m s}^{-1}$ in the direction opposite to the force. What is the final velocity of the body in the direction of the applied force?

$11\text{ m s}^{-1}$ Answer
B
$21\text{ m s}^{-1}$
C
$16\text{ m s}^{-1}$
D
$43\text{ m s}^{-1}$

Answer

The final velocity of the body in the direction of the force is

11\text{ m s}^{-1}

By the impulse-momentum theorem, the impulse

F \Delta t = 12 \times 4.0 = 48\text{ N s}

causes a velocity change

\Delta v = \frac{48}{3.0} = 16\text{ m s}^{-1}

in the direction of the force. Since the body initially moved in the opposite direction at

-5.0\text{ m s}^{-1}

, the final velocity is

-5.0 + 16 = 11\text{ m s}^{-1}

in the direction of the force.

Step-by-Step Solution

Assign direction signs to physical quantities based on a chosen coordinate system.

Let the direction of the applied force be positive (+). Then

F = +12\text{ N}

m = 3.0\text{ kg}

t = 4.0\text{ s}

, and initial velocity

u = -5.0\text{ m s}^{-1}

Velocity and force are vector quantities; motion opposite to the force must carry a negative sign.

Calculate the impulse delivered by the force.

\text{Impulse} = F \times \Delta t = 12\text{ N} \times 4.0\text{ s} = 48\text{ N s}

Impulse equals force multiplied by the time interval over which it acts.

Apply the impulse-momentum theorem

F \Delta t = m(v - u)

to solve for final velocity

v

48 = 3.0 \times (v - (-5.0)) \implies 16 = v + 5.0 \implies v = 11\text{ m s}^{-1}

The change in linear momentum of an object is equal to the net impulse applied to it.

Key Concept

Impulse-Momentum Theorem and Vector Sign Conventions

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