Question

An object is moving on a straight line according to the equation s=3t2

+4t+5, when s is

measured in meter and t in sec. Find instantaneous velocities at 2 and 3 seconds also find out

acceleration of a body.​

Answer 1

Explanation:

dS/dt = dv

=> d(3t² + 4t + 5)/dt = dv

=> 3(2t) + 4(1) + 0 = dv

=> 6t + 4 = dv

At t = 2, v = 6(2) + 4 = 16 m/s

t = 3, v = 6(3) + 4 = 22 m/s

Also, now,

=> v = 6t + 4

=> dv/dt = d(6t + 4)/dt

=> da = 6(1) + 0

=> da = 6

Acceleration is 6 m/s²

Answer 2

$\huge{hello}$

$s = 3 {t}^{2} + 4t + 5$

$instantaneous \: velocities = ds/dt = (3 {t}^{2} + 4t + 5)/dt$

$v = 2 \times 3t + 4$

$v = 6t + 4$

$instantaneous \: velocities \: at \\ \: 2 \: sec = 6(2) + 4$

$= 12 + 4 = 16 \: ms {}^{ - 1}$

$instantaneous \: velocities \: at \: 3 \: sec = \\ 6(3) + 4$

$=1 8 + 4 = 22 ms{}^{ - 1}$

$acceleration = dv/dt = (6t + 4)/dt \\ a = 6 {ms}^{ - 2}$

$acceleration \: is \: constant \: here \: not \: dependtent \: on \: time \:$

$so, \: acceleration \: at \: 2 \: and \: 3 \: seconds \: is \: 6 {ms}^{ - 2}$