From the The velocity-time graph for an ice skater is shown in Figure ,
The distances covered by the skater between 0 s and 2 s is 2 meters
The distance covered by the skater between 2 s and 5 s is 6.25 meters
What is Velocity?
The total displacement covered by any object per unit of time is known as velocity. It depends on the magnitude as well as the direction of the moving object. The unit of velocity is meter/second. It can also be represented by the infinitesimal rate of change of displacement with respect to time. The generally considered unit for velocity is a meter per second.
As we know that slope of the velocity time curve represents the acceleration of the object while the area under the velocity time curve represents the displacement covered by the object
As given in the problem The velocity-time graph for an ice skater is shown in Figure
the distance covered by the skater between 0 s and 2 s is
The area of the triangle formed between 0 s and 2 s
Distance = 1/2 ×2×2
= 2 meters
Similarly, the distance covered by the skater between 2 s and 5 s is the area of the quadrilateral formed between 2 s and 5 s
Distance between 2 s and 5 s = area of the quadrilateral
Area of the quadrilateral = area of the square between 2s and 4s + area of the triangle between 2 s and 4 s + area of the triangle between 4 s and 5 s + area of the square between 4 s and 5 s
= 2×2 + 1/2 ×2×1/2 + 1/2 ×1×3/2 + 1×1
=4 + 1/2 + 3/4 +1
=6.25 meters
Thus, The skater travels a distance of 2 meters between 0 and 2 seconds and The skater travels 6.25 meters between seconds 2 and 5.
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