Suppose quantity s is a length and quantity t is a time. suppose the quantities vand aare defined by v = ds/dt and a = dv/dt. (a) what is the dimension of v? (b) what is the dimension of the quantity a?
what are the dimensions of (c)vdt, (d) a dt, and (e) da/dt?

Explanation:

(a) Velocity is given by :

s is the length of the distance

t is the time

The dimension of v will be,      

(b) The acceleration is given by :

v is the velocity

t is the time

The dimension of a will be,

(c) Since,

(d) Since,

(e)

Hence, this is the required solution.

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note: the given question is incomplete.

complete question is given below.

which is an example of kinetic energy?

a. the energy stored in ethanol  

b. a hockey puck sliding across the ice  

c. a compressed spring  

d. a ball sitting at the top of a ramp

solution: the kinetic energy is the energy posses by the virtue of the motion of the object.

in the given options, a, c and d are the example of potential energy because it is the energy posses by the virtue of the rest of the object. but option b has the kinetic energy as the object is in motion.

hence, a hockey puck sliding across the ice   is the apex example of kinetic energy.

so, the option (b) a hockey puck sliding across the ice   is the correct option.