Velocity Time Graphs
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Either paper 5 marks
The velocity-time graph shows \(18\) seconds of a car's journey along a straight road.
(a)Write down the greatest velocity of the car.
(b)Work out the acceleration of the car during the first \(4\) seconds.
(c)Work out the deceleration of the car during the last \(8\) seconds.
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Either paper 2 marks
A passenger plane flies at a constant speed of 550 miles per hour for 3 hours 45 minutes.
Here is a grid with time in hours across and speed in mph up.
On the grid, draw a speed-time graph to represent this information.
Plot the point at each end of the graph, then join them.
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Either paper Higher5 marks
A train sets off from a station, travels at a steady velocity, then slows to a stop at the next station.
(a)Calculate the distance the train travels while it is moving at a steady velocity.
(b)Calculate the total distance the train travels in the \(20\) seconds.
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Either paper Higher5 marks
A van is travelling along a straight road. The graph shows its velocity over \(10\) seconds.
(a)Work out the deceleration of the van between \(4\) seconds and \(6\) seconds.
(b)Work out the distance the van travels between \(4\) seconds and \(6\) seconds.
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Either paper Higher3 marks
Ella ran a 168 metre race. The graph shows the first 13 seconds of her race.
After 13 seconds she kept running at the speed she had reached at the end of the graph until she crossed the finish line.
Ruth completed the race in 28.5 seconds.
Did Ella finish before Ruth? You must show your working.
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Either paper Higher4 marks
The graph shows the speed, in metres per second, of an object \(t\) seconds after it started to move from rest.
(a)Using four trapeziums of equal width, find an estimate for the area under the graph between \(t = 1\) and \(t = 5\).
(b)What does this area represent?
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Either paper Higher5 marks
A car joins a motorway from rest. The graph shows its velocity for the first \(12\) seconds.
(a)Work out the acceleration of the car between \(4\) seconds and \(6\) seconds.
(b)Work out the total distance the car travels in the \(12\) seconds.
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Either paper Higher6 marks
Grace rides a bike in a straight line for \(11\) seconds.
The graph shows her speed.
(a)Show that the distance Grace rides is more than \(60\) metres.
(b)Calculate her average acceleration for the first \(10\) seconds.
State the units of your answer.
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Either paper Higher4 marks
Hafsa rides a \(150\) metre sprint on a cycle track. Timing starts as she passes the start line, and she crosses the finish line \(12\) seconds later.
The graph shows her speed for the first \(6\) seconds.
For the last \(6\) seconds her speed changes at a constant rate. Hafsa crosses the finish line at \(v\) m/s.
Calculate the value of \(v\).
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Either paper Higher5 marks
A train leaves a station and travels along a straight track.
It accelerates uniformly from rest to \(12\) m/s in \(8\) seconds.
It then travels at a steady \(12\) m/s for \(90\) seconds.
It then decelerates uniformly, coming to rest at the next station after a further \(10\) seconds.
(a)Work out the total distance the train travels.
(b)Work out the average speed of the train for the whole journey.
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(a) \(16\ \text{m/s}\)
(b) \(4\ \text{m/s}^2\)
(c) \(2\ \text{m/s}^2\) - A horizontal line from \((0, 550)\) to \((3.75, 550)\)
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(a) \(160\ \text{m}\)
(b) \(240\ \text{m}\) -
(a) \(1\ \text{m/s}^2\)
(b) \(22\ \text{m}\) - No: Ella finishes in 29 s and Ruth in 28.5 s.
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(a) \(54\) m
(b) The distance travelled, in metres, by the object between \(t = 1\) and \(t = 5\) seconds -
(a) \(3\ \text{m/s}^2\)
(b) \(242\ \text{m}\) -
(a) Triangle \(28\) m plus rectangle \(32\) m gives \(60\) m; the curve is above the straight line, so the distance is more than \(60\) m
(b) \(0.8\ \text{m/s}^2\) - \(10\ \text{m/s}\)
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(a) \(1188\ \text{m}\)
(b) \(11\ \text{m/s}\)
Takes a couple of seconds the first time a sheet is made.