Question

A car acquires a velocity of 72 kmh⁻¹ in 10 s starting from rest. Calculate :
(i) the acceleration
(ii) the average velocity
(iii) the distance travelled in this time.

Answer 1

(i) acceleration = 2 m/s2

(ii) average velocity  = 10 m/s

(iii) distance travelled = 100 m

Explanation:

final velocity v = 72 km/h = 72 * 1000 / (60 * 60) = 20 m/s

t = 10 s

u = 0

Equation of motion, we know v = u + at

20 = 0 + 10a

a = 20/10 = 2 m/s2

Displacement = distance travelled = s

Equation of motion, v^2 - u^2 = 2as

20^2 = 2 * 2 * s

s = 400 / 4 = 100 m.

Average velocity = displacement / time = 100 / 10 = 10 m/s

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

u = 0 (Initial velocity) [Because car starts from rest]

Also,

v (Final velocity) = 72 km/h

= 72 × 5/18

= 20 m/s

t (Time taken) = 10 seconds

Now,

Using 1st Equation of motion :-

v = u + at

⇒ 20 = 0 + a × 10

⇒ 20 = 10a

⇒ 20/10 = a

⇒ a = 2 m/s²

Also,

Using 2nd Equation of motion :-

s = ut + 1/2 × at²

⇒ s = 0 × 10 + 1/2 × 2 × 10 × 10

⇒ s = 1/2 × 200

⇒ s = 100

Now,

As we know that,

Average velocity = Distance/Time

= 100/10

= 10 m/s