Question

the speed time graph of a car is shown in figure the ratio of distance travelled by the car in first 5 second and next 5 second is​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Ratio=1:3}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Final \: speed = 15 \: m/s \\ \\ \tt: \implies Time = 10 \: s \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies \frac{ s_{(at \: t = 5 \: sec)}}{s_{(at \: t =next \: 5 \: sec)}} = ?$

• According to given question :

$\tt \circ \: Initial \: velocity = 0 \: m/s \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies v = u + at \\ \\ \tt: \implies 15 = 0 + a \times 10 \\ \\ \tt: \implies \frac{15}{10} = a \\ \\ \green{\tt: \implies a = 1.5 { \: m/s}^{2} } \\ \\ \bold{For\:distance \: travel \:in \: first \: 5 \: sec} \\ \tt: \implies s_{(at \: t = 5)} = ut + \frac{1}{2} {at}^{2} \\ \\ \tt: \implies s_{(at \: t = 5)} = 0 \times 5 + \frac{1}{2} \times 1.5 \times {5}^{2} \\ \\ \tt: \implies s_{(at \: t = 5)} =18.75 \: m - - - - - (1) \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies v = u + at \\ \\ \tt : \implies v = 0 + 1.5 \times 5 \\ \\ \tt : \implies v =7.5 \: m/s$

$\tt \circ \: Initial \: velocity_{(at \: t = 5 \: sec)} = 7.5 \: m/s \\ \\ \bold{Similarly \: for \: next \: 5 \: sec : } \\ \tt: \implies s_{(at \: t = next \: 5 \: sec)} =ut + \frac{1}{2} {at}^{2} \\ \\ \tt: \implies s_{(at \: t = next \: 5 \: sec)} =7.5 \times 5 + \frac{1}{2} \times 1.5 \times {5}^{2} \\ \\ \tt: \implies s_{(at \: t = next \: 5 \: sec)} =37.5 + 18.75 \\ \\ \tt: \implies s_{(at \: t = next \: 5 \: sec)} =56.25 \: m - - - - - (2)\\ \\ \bold{For \: Ratio : } \\ \tt: \implies \frac{ s_{(at \: t = 5 \: sec)}}{s_{(at \: t =next \: 5 \: sec)}} = \frac{18.75}{56.25} \\ \\ \green{\tt: \implies \frac{ s_{(at \: t = 5 \: sec)}}{s_{(at \: t =next \: 5 \: sec)}} = \frac{1}{3} }\\\\ \green{\tt \therefore Ratio=1:3}$