Question

A car accelerates from 20 m/s to 30 m/s in 10 s. (a) Calculate the car’s acceleration using v = u + at. (b) Draw a velocity–time graph to show the car’s motion. Find the distance it travels by calculating the area under the graph. (c) Check your answer by using the equation s = ut + ½at2 

Answer 1

Initial velocity $(u)=20\space m/s$

Final velocity $(v)=30\space m/s$

Time taken $(t)=10\space s$

Acceleration $= a\space m/s^2$

$(a)\space a=\dfrac{v-u}{t}\\\Rightarrow a=1\space m/s^2$

$(b)\space$

Distance covered $(s)=Area\space under \space the\space curve=(20\times10)+(\dfrac{1}{2}\times10\times10)$

$s=250\space m$

$(c)\space s=ut+\dfrac{1}{2}at^2\\\Rightarrow s=20\times10+\dfrac{1}{2}\times1\times100\\\Rightarrow s=250\space m$