Question

A body moving with uniform acceleration along a straight line covers 60m in the 5^th second and 80m in the 8^th second of its motion. Calculate the initial velocity and uniform acceleration.

Answer 1

The distance travelled during the nth second is given by,

s_n = u + a/2(2n – 1), n = 5 and s_n = 60

∴ 60 = u + a/2 (2 × 5 – 1)

60 = u + 9a/2 ………… (1)

Similarly, for n = 8, s_n = 80

∴ 80 = u + a/2 (2 × 8 – 1)

80 = u + 15a/2 …………….. (2)

(2) – (1), gives

20 = 6a/2 = 3a

∴ a = 20/3 ms^-2

Using this in equation (1), we get

60 = u + (9 x 20)/(2 x 3)

u = 60 – 30 = 30 ms^-1