A cat walks in a straight line, which we shall call the x -axis with the positiv

Question

A cat walks in a straight line, which we shall call the x-axis with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time.

What distance does the cat move from t=0 to t=7.5s?

Answer: 26cm.

I have already exhausted the 9 tries allowed in this problem. I have no clue how to arrive at the correct answer displayed. The following is my attempt:

x = 0+8(7.5)+[(-4/3)(7.5^2)]/2 = 22.5cm

I don't understand. Do I need to split the equations from t: [0,6] and then t: [6,7.5] somehow? Please explain.

A cat walks in a straight line, which we shall call the x-axis with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time.

Explanation / Answer

Eqyation of velocity of the line = v = -4/3t +8

put t= 7.5 we get v=-2 ;

total distance travelled = total area under the grah of v vs t :

= 0.5 * 8*6 + 0.5*2 *1.5 =25.5 cm is the answer !

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