A body moving with uniform acceleration along a straight line covers 6

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

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

Answer»

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