PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A toy car moves along a straight track. A rough sketch of its velocity v(t) (in cm/s) versus time t (in s) is drawn on a square grid.
• The t–axis is horizontal with tick marks every 2s.
• The v–axis is vertical with tick marks every 1cm/s.
• The graph begins at (0,0), rises linearly to (4,4), then descends linearly to (8,−2), and finally rises linearly to (10,0).
• The region between the curve and the t–axis for 0≤t≤10 is lightly shaded to suggest the net area.
• Counting complete grid squares, the shaded region that lies above the t–axis contains about 14 full squares, while the part that lies below the axis contains about 5 full squares.
Answer the following questions about the car’s motion on the interval 0≤t≤10.
(a) Explain whether the car’s net displacement over the 10-second interval is determined by adding or subtracting the area that lies below the t–axis. Justify using the meaning of signed area.
(b) State the units of the net displacement and describe how those units are obtained from the graph’s axes.
(c) Using the grid-square information provided, estimate the car’s net displacement during the interval 0≤t≤10. Show your reasoning and include units.