Chapter 3, Problem 61A

To determine

The final velocity of a proton.

Answer to Problem 61A

  $v_f=0.7\times {10}^5\text{m/s}$

Explanation of Solution

Given:

Initial velocity of the proton is $2.35\times {10}^5\text{m/s}$ , and it is uniformly acceleration at the rate of $-1.10\times {10}^{12}{\text{m/s}}^{\text{2}}$ for $1.50\times {10}^{-7}\text{s}$ .

Formula used:

Final velocity with constant acceleration can be obtained by,

  $v_f=v_i+a\Delta t$

Where, $v_f$ is the final velocity, $v_i$ is the initial velocity, a is the acceleration and $\Delta t$ is the time taken.

Calculation:

Using the given values in above formula, the final velocity of proton is:

  $\begin{array}{c}{v}_f=\left(2.35\times {10}^5\right)+\left(\left(-1.10\times {10}^{12}\right)\left(1.50\times {10}^{-7}\right)\right)\\ =\left(2.35-1.65\right)\times {10}^5\\ =0.7\times {10}^5\text{m/s}\end{array}$

Conclusion:

Thus, the final velocity of the proton is $0.7\times {10}^5\text{m/s}$ .