A cyclist travels at a constant velocity of 4.5 m/s westward, then speeds up with a steady acceleration of 2.3m/s2. Calculate the cyclist’s speed after accelerating for 5.0 s.

To find the cyclist's speed after accelerating, we can use the formula for final velocity: \[ v_f = v_i + a \cdot t \] where: - \( v_f \) is the final velocity, - \( v_i \) is the initial velocity, - \( a \) is the acceleration, - \( t \) is the time. Given: - \( v_i = 4.5 \, \text{m/s} \) (initial velocity, westward), - \( a = 2.3 \, \text{m/s}^2 \) (acceleration), - \( t = 5.0 \, \text{s} \) (time). Substituting the values into the formula: \[ v_f = 4.5 \, \text{m/s} + (2.3 \, \text{m/s}^2 \cdot 5.0 \, \text{s}) \] Calculating the acceleration distance: \[ 2.3 \, \text{m/s}^2 \cdot 5.0 \, \text{s} = 11.5 \, \text{m/s} \] Now adding that to the initial velocity: \[ v_f = 4.5 \, \text{m/s} + 11.5 \, \text{m/s} = 16.0 \, \text{m/s} \] So, the cyclist's speed after accelerating for 5.0 seconds is: \[ \boxed{16.0 \, \text{m/s}} \] (still moving westward).