Question

find the distance travelled by a car with a velocity v(t) = 2t + 5 where t is in hours and v is in km h -1 for the first hours

Answer 1

Answer :

• 6 km

Given :

• A car is moving with a velocity , v(t) = 2t + 5 where t is in hours and v is in km-h⁻¹

To Find :

• Distance travelled for 1 hour

Solution :

• We know that velocity is defined as displacement per time .

$\implies \bf v=\dfrac{ds}{dt}\\\\\implies \bf s=\int\limits^1_0 v\;dt\\\\\implies \bf s=\int\limits^1_0 (2t+5)\;dt\\\\\implies \bf s=2.\dfrac{t^2}{2}\bigg]\limits^1_0+5t\bigg]\limits^1_0\\\\\implies \bf s=(1^2-0^2)+5(1-0)\\\\\implies \bf s=1+5\\\\\implies \bf s=6\;km$