Newton's Second Law — SUV Accelerating from Rest (Worked Example)

Easy

Problem

A 1500 kg SUV accelerates from rest to 20 m/s in 8.0 s on a level road. (a) What is its average acceleration? (b) What net forward force is required (ignoring drag)?

Free-body diagram of the accelerating SUV (vertical forces balanced).

Given

m = 1500 kg
u = 0 m/s (starts from rest)
v = 20 m/s
t = 8.0 s

Find

Average acceleration a and net force F.

Principle

Average acceleration is the change in velocity divided by time, and Newton's second law (F = ma) links that acceleration to the net force causing it.

Formula

a = \frac{v - u}{t}, \qquad F = ma

a = (v − u)/t and F = ma

Solution

Find acceleration: $a = (v - u)/t = (20 - 0)/8.0$
Calculate: $a = 20/8.0 = 2.5\ \mathrm{m/s^2}$
Apply Newton's second law: $F = ma = 1500 \times 2.5$
Multiply: $F = 3750\ \mathrm{N}$ forward

a = 2.5 m/s²; F = 3.75 × 10³ N forward

Unit check

(m/s)/s = m/s² for acceleration; kg × m/s² = N for force. Both match — dimensionally consistent.

What this means physically

The engine must deliver a net 3750 N — roughly the weight of a 380 kg mass — to achieve that acceleration. Real engines push harder, since part of their effort fights air drag and rolling resistance.

Common mistake

Using F = ma with the engine's full thrust instead of the net force. Drag and friction subtract first; only what remains accelerates the car.