Question

A particle moves along x-axis such that its velocity (v) varies with time (t) as v = (4t – t2) m/s. The distance travelled by the particle from t = 0 to t = 6 s is

Answer 1

Given : A particle moves along x-axis such that its velocity (v) varies with time (t) as v = (4t – t²) m/s  

To Find : The distance travelled by the particle from t = 0 to t = 6 s

Solution:

Velocity = rate of change of displacement

=>v = ds/dt

=> ds  = vdt

v= 4t - t²

=> ds = (4t - t²)dt

integrating both sides

$s=\int\limits^6_0 {(4t-t^2)} \, dt$

$s=\big[\dfrac{4t^2}{2}-\dfrac{t^3}{3}\big]^6_0$

$s=\big[2t^2-\dfrac{t^3}{3}\big]^6_0$

s= 2(6)² - 6³/3  - 0

S = 72 - 72

s = 0  

The distance travelled by the particle from t = 0 to t = 6 s  is 0 m

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