A car moves with a constant velocity of 10 ms^–1 for 10 s along a straight track, then it moves with uniform acceleration of 2 ms^–2 for 5 seconds. Find the total displacement and velocity at the end of the 5th second of acceleration.

Let v₁ and t₁ be the initial velocity and the time for the first part where the car is moving with a constant velocity.

t₁ = 10 s; v₁ = 10 m s^–1

∴ Distance travelled s₁ = v₁ t₁

i.e., s₁ = 10 × 10 = 100 m

For the second part, i.e., when the car accelerates,

a = 2 m s^–2, v =?

t = 5 seconds s₂ =?

u = 10 m s^–1

v = u + at

v = 10 + 2 × 5

v = 10 + 10

Þ v = 20 ms^–1

$$\begin{gathered} {\mathrm{s}}_2=\mathrm{ut}+\frac{1}{2}{\mathrm{at}}^2 \\ {\mathrm{s}}_2=10\times 5+\frac{1}{2}\times 2\times 5^2 \\ =50+1\times 25=50+25=75 \mathrm{m} \\ \text{ Total displacement }\mathrm{s}={\mathrm{s}}_1+{\mathrm{s}}_2 \\ \therefore \mathrm{s}=100+75=175 \mathrm{m}. \end{gathered}$$