Question

A motor car takes 10 second to cover 30 minute & 12 second to cover 42 meter find the uniform acceleration

Answer 1

A motor car takes 10s to cover 30m and 12 sec to cover 42m, then we have to find uniform acceleration.

let u is initial velocity and a is acceleration of motor car.

using formula, S = ut + 1/2 at²

case 1 : t = 10s , S = 30m

so, 30m = u(10) + 1/2 a(10)²

⇒30 = 10u + 50a

⇒ 3 = u + 5a ........(1)

velocity after 10s , v = u + a(10) = u + 10a

case 2 : t = 12s , S = 42m

so, 42 = v(12) + 1/2a(12)²

⇒42 = 12(u + 10a) + 1/2 a(144)

⇒42 = 12u + 120a + 72a

⇒42 = 12u + 192a

⇒7 = 2u + 32a ......(2)

solving equations (1) and (2),

eq(2) - 2 × eq(1)

7 - 2 × 3 = 2u + 32a - 2(u + 5a)

⇒1 = 2u + 32a - 2u - 10a

⇒1 = 22a

⇒a = 1/22 = 0.04545 m/s²

hence, acceleration of motor car is 0.04545m/s²