Question

a) How is the sign of ACCELERATION represented on a velocity vs time graph.

b) Why is acceleration positive even though a cart is slowing down on a track. Explain in term of a) a mathematician would find acceptable b) a younger sibling would understand

Answer 1

A)

As we know that acceleration = dv/dt .

Now if we assume the +ve acceleration than we can say that dv/dt is +ve i.e. that velocity vs time graph has a +ve slope.

And if assume the -ve acceleration than we can say that dv/dt is -ve i.e. that velocity vs time graph has a -ve slope.

for zero acceleration than we can say that dv/dt = 0 i.e. slope is zero.

for better understanding i m uploaded an image-

B)-

As mentioned that acceleration is +ve but cart is slowing down i.e that velocity and acceleration of cart are in the opposite direction than only cart will slow down.

In mathematics -

V = U + at

for slowing down, V = 0

0 = U + at

at = -U (a>0 and t>0)

i.e that initial velocity is in opposite direction.

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