A 2015 Porsche 918 Spyder accelerates from 0 to 88 ft/sec (60 mph) in 2.2 seconds, the fastest a

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A 2015 Porsche 918 Spyder accelerates from 0 to 88 ft/sec...

A 2015 Porsche 918 Spyder accelerates from 0 to 88 ft/sec $(60 \mathrm{mph})$ in 2.2 seconds, the fastest acceleration of any car available for retail sale in $2015 .^{1}$ (a) Assuming that the acceleration is constant, graph the velocity from $t=0$ to $t=2.2$ (b) How far does the car travel during this time?

A 2015 Porsche 918 Spyder accelerates from 0 to 88 ft/sec $(60 \mathrm{mph})$ in 2.2 seconds, the fastest acceleration of any car available for retail sale in $2015 .^{1}$
(a) Assuming that the acceleration is constant, graph the velocity from $t=0$ to $t=2.2$
(b) How far does the car travel during this time?

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Key Concepts

Displacement Calculation

Displacement in uniformly accelerated motion can be determined by calculating the area under the velocity-time graph, often by using formulas for the area of geometric shapes or by integrating the velocity function with respect to time. This technique directly connects the graphical representation of motion with quantitative measures of distance.

Velocity-Time Graph

A velocity-time graph under constant acceleration is a straight line where the slope represents the constant acceleration. The area under this graph corresponds to the displacement, making it a valuable visual tool for understanding and calculating how far an object has traveled.

Constant Acceleration

This concept means that the change in velocity over time remains uniform throughout the motion. In problems like this, assuming constant acceleration simplifies the analysis because it allows the use of linear equations to relate velocity, time, and displacement.

Kinematics Equations

Kinematics equations for constant acceleration are mathematical relationships that link displacement, initial velocity, time, and acceleration. They are essential tools for solving motion problems, such as computing the distance traveled or the final velocity when acceleration is known.

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