During a short interval of time the speed v in m/s of an automobile is given by v = at² + bt³, where the time t is in seconds.The units of a and b are respectively: A)m*s²; m*s⁴ B)s³/m; s⁴/m C)m/s²; m/s³ D)m/s³; m/s⁴ E)m/s⁴; m/s⁵

Question

Quizplus · Accepted Answer

The expression given for velocity (v) is v = atS1U1P12S1S1P0 + btS1U1P13S1S1P0. We know that the units of velocity are m/s and time is in seconds, therefore a and b must have units that cancel out the dimensions of tS1U1P12S1S1P0 and tS1U1P13S1S1P0 respectively, leaving us with the correct dimensions of m/s.

For the first part of the expression (atS1U1P12S1S1P0), we can see that it has a dimension of m/s2*S1U1P12S1S1P0, which means that we need units of F1F1F1S1F1F1F10sS1U1P1X for 'a' to cancel out the dimensions of tS1U1P12S1S1P0 .

For the second part of the expression (btS1U1P13S1S1P0), we can see that it has a dimension of m/s2*S1U1P13S1S1P0, which means that we need units of F1F1F1S1F1F1F10sS1U1P1Y for 'b' to cancel out the dimensions of tS1U1P13S1S1P0.

Therefore, the units of a and b respectively should be m/s2*S1U1P12S1S1P0 and F1F1F1S1F1F1F10sS1U1P13S1S1P0 which is equivalent to m/s*S1U1P13S1S1P0. So the correct option is D.

During a Short Interval of Time the Speed V in M/s