Question

A car starts from rest with an acceleration of 6

Answer 1

Answer:

$t=16.67s$

Explanation:

From the question, acceleration from $6m/s^2 \ to \ 0m/s^2$ in 10 seconds.

Acceleration function can be written as:-

$a_t=6-0.6t$

From the acceleration equation, we can obtain the velocity equation:

$v(t)=\int\limits^t_b {0} \, dv=\int\limits^t_0 {a(t)} \, dt\\v(t)=\int\limits^t_0 {(6-06t)} \, dt=6t-0.3t^2\\*dv=a(t)dt$

We calculate velocity after 10sec from the above v(t) as $30m/s$.

To obtain distance travelled after 10 seconds:-

$S=\int\limits^{10}_0 {6t-0.3t^2} \, dt=|3t^2-0.1t^3| \ *lims(10,0)\\ S=200m$

Therefore 200m is for 10seconds, and next 200m at 30m/s

Total time=$10+\frac{200}{30}=16.67s$