Question

10. Given that the total distance travelled is 4 km and that the initial aceleration is 4 m/s², find:a) the value of V.b) the value of T.

Answer 1

The initial deceleration is 4 m/s^2, so this means that considering the first line segment, $\frac{V-100}{T}=-4 \implies V=100-4T$.

The total distance traveled is 4 km, which is equal to 4000 meters. This is equal to the area under the graph, so $400T-\frac{1}{2}(100-V)(5T)=4000$.

$400(100-4T)-\frac{1}{2}(4T)(5T)=4000\\\\40000-1600T-10T^2=4000\\\\10T^2 +1600T-36000=0\\\\T^2 +160T-3600=0\\\\(T+180)(T-20)=0\\\\T=20 (T > 0)\\\\\therefore V=100-4(20)=20$