A small electric car travels around a level circular test track of radius

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

50\,\text{m}

. A data-acquisition system measures the car’s instantaneous speed

v

and the corresponding magnitude of its acceleration

a_c

directed toward the track’s center. The student plans to construct two separate graphs from the same set of measurements: • graph 1:

a_c

on the vertical axis versus

v

on the horizontal axis • graph 2:

a_c

on the vertical axis versus

v^{2}

on the horizontal axis Assume the car’s motion remains uniform and the tyres do not skid. (a) Describe qualitatively the shape and intercept of graph 1 that the student should expect. Justify your answer without performing a numerical calculation. (b) Explain why plotting

a_c

versus

v^{2}

(graph 2) instead of

v

is advantageous for analyzing the data. In your explanation, write the mathematical relationship between

a_c

and

v^{2}

and identify the physical meaning of the slope. (c) Suppose the best-fit line for graph 2 yields a slope of

0.020\,\text{m}^{-1}

. Interpret the numerical value and units of this slope in the context of the experiment, and state whether the track radius determined from the graph is consistent with the manufacturer’s quoted value of

50\,\text{m}

. Support your conclusion with reasoning.

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