Question

A car was travelling at a constant speed of 19 m/s, then accelerated for 10 seconds. The distance travelled, during this time, "d" metres, is given by the formula d = 19t + t^2, where "t" is the time in seconds since the acceleration began. How long did it take the car to travel 200m? Give the answer to the nearest tenth of a second. Solve algebraically.

Answer 1

7.5 seconds.

Explanation:

Substitute the distace 220m in the given equation:

d = 19t + t^2

200 = 19t + t^2

t^2 + 19t - 200 = 0

t = [-19 +/- sqrt(19^2 - 4*1*-200)] / 2

t = -19 +/- sqrt(1161) / 2

t = ( -19 +/- 34.07) / 2

t = 7.535 seconds