Question

The displacement of a body at any time t after starting is given by s = 15t-0.4t2. find the time when the velocity of the body will be e 7 m per second

Answer 1

$10 \: s$

Explanation:

$Given, \: \: \: s = 15t - 0.4 {t}^{2} \: \: \: and \: \: \: v = 7 \: m {s}^{ - 1} \\ we \: \: know \: \: \boxed{v = \frac{ds}{dt} } \\ Now, \: \: v = \frac{d(15t - 0.4 {t}^{2} )}{dt} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 15 - 2 \times 0.4t \\ \: \: \: \: \: \: = 15 - 0.8t \\ A/Q, \: \: \: \: \: v = 7 \: m {s}^{ - 1} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 7 = 15 - 0.8t \\ \: \: \: \: \: \: \: \: \: \: 0.8t = 15 - 7 \\ 0.8t = 8 \\ \: \: \: \: \: \: \: \: \: \: t = \frac{8}{0.8} \\ \: \: \: \: \: \: \: \: \: \: \: \boxed{ t = 10 \: s}$